Details

Time bar (total: 9.2s)

sample16.0ms

Algorithm
intervals
Results
7.0ms279×body80valid

simplify72.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0911
12111
23910
36310
49310
512510
612710
done12710

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.0b

localize7.0ms

Local error

Found 2 expressions with local error:

3.5b
(* y (+ 1.0 (* z z)))
4.3b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 74
Calls
2 calls:
7.0ms
(* y (+ 1.0 (* z z)))
7.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series109.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(* y (+ 1.0 (* z z)))
58.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify609.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (187.0ms)

IterNodesCost
01601102
14151075
21394856
done5000856

prune199.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (fma z z 1.0))) (sqrt (+ 1.0 (* z z))))
4.3b
(/ (/ 1.0 x) (* (* y (sqrt (fma z z 1.0))) (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (fma z z 1.0))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-exp-log add-cbrt-cube
25×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
13×associate-/l*
11×pow1
9×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod
6×sqrt-div associate-*r*
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×flip3-+ pow-prod-down flip-+ div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative hypot-def associate-/l/
Counts
4 → 112
Calls
4 calls:
14.0ms
(* (* y (sqrt (fma z z 1.0))) (sqrt (+ 1.0 (* z z))))
15.0ms
(/ (/ 1.0 x) (* (* y (sqrt (fma z z 1.0))) (sqrt (+ 1.0 (* z z)))))
1.0ms
(sqrt (fma z z 1.0))
3.0ms
(sqrt (+ 1.0 (* z z)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (* y (sqrt (fma z z 1.0))) (sqrt (+ 1.0 (* z z))))
97.0ms
(/ (/ 1.0 x) (* (* y (sqrt (fma z z 1.0))) (sqrt (+ 1.0 (* z z)))))
54.0ms
(sqrt (fma z z 1.0))
42.0ms
(sqrt (+ 1.0 (* z z)))

simplify941.0ms

Counts
124 → 124
Iterations

Useful iterations: 2 (396.0ms)

IterNodesCost
02212308
15851601
223501360
done50001360

prune342.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1.0 x))
0.6b
(cbrt (/ 1.0 x))
1.4b
(/ (cbrt (/ 1.0 x)) (fma z z 1.0))
4.9b
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt (/ 1.0 x)) (fma z z 1.0)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
192×times-frac
134×add-sqr-sqrt
121×cbrt-prod
110×add-cube-cbrt *-un-lft-identity
52×associate-*r*
27×add-exp-log
19×add-cbrt-cube
16×associate-/l*
12×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
7×associate-*l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-div associate-/r*
2×pow1/3
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 223
Calls
4 calls:
1.0ms
(cbrt (/ 1.0 x))
1.0ms
(cbrt (/ 1.0 x))
9.0ms
(/ (cbrt (/ 1.0 x)) (fma z z 1.0))
44.0ms
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt (/ 1.0 x)) (fma z z 1.0)))

series716.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(cbrt (/ 1.0 x))
198.0ms
(cbrt (/ 1.0 x))
187.0ms
(/ (cbrt (/ 1.0 x)) (fma z z 1.0))
131.0ms
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt (/ 1.0 x)) (fma z z 1.0)))

simplify1.4s

Counts
235 → 235
Iterations

Useful iterations: 2 (740.0ms)

IterNodesCost
03334661
18464472
232844017
done50004017

prune772.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1.0 (cbrt x)))
1.0b
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt (/ 1 (* (cbrt x) (cbrt x)))) (sqrt (fma z z 1.0))))
14.7b
(sqrt (fma z z 1.0))
14.7b
(sqrt (fma z z 1.0))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
110×add-sqr-sqrt
85×cbrt-prod
64×*-un-lft-identity associate-*r*
60×add-cube-cbrt
44×sqrt-prod
25×add-exp-log
18×add-cbrt-cube unswap-sqr
9×div-inv
8×pow1 prod-exp cbrt-unprod
7×cbrt-undiv div-exp associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times cbrt-div pow1/3 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 178
Calls
4 calls:
2.0ms
(cbrt (/ 1.0 (cbrt x)))
52.0ms
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt (/ 1 (* (cbrt x) (cbrt x)))) (sqrt (fma z z 1.0))))
1.0ms
(sqrt (fma z z 1.0))
1.0ms
(sqrt (fma z z 1.0))

series957.0ms

Counts
4 → 12
Calls
4 calls:
280.0ms
(cbrt (/ 1.0 (cbrt x)))
566.0ms
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt (/ 1 (* (cbrt x) (cbrt x)))) (sqrt (fma z z 1.0))))
59.0ms
(sqrt (fma z z 1.0))
52.0ms
(sqrt (fma z z 1.0))

simplify1.1s

Counts
190 → 190
Iterations

Useful iterations: 2 (538.0ms)

IterNodesCost
03544623
19154332
231444049
done50004049

prune703.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 4.8b

regimes285.0ms

Accuracy

0% (1.6b remaining)

Error of 6.2b against oracle of 4.7b and baseline of 6.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11111
done1111

end0.0ms

sample403.0ms

Algorithm
intervals
Results
236.0ms8608×body80valid